Transcript Money Demand (Handa, Chapter 2)

Money Demand
(Handa, Chapter 2)
Monetary Theory and Policy
Graduate Seminar ECON 6411
Fall 2008
1
First Lessons
Hicks (1967), Critical Essays in Monetary Theory,
Oxford University Press.
 Uses the model of a medieval market fair
 Claims to have constructed a system with money
as a medium of exchange, but not as a store of value.
Problem: Money is a store of value for the market
period.
2
First and Second Principles
 A First Principle of Monetary Theory is:
Money is a store of value. There are things that act as stores of
value that are not money, but there are no forms of money that
are not stores of value.
 A Second Principle of Monetary Theory is:
A crucial difference between barter and monetary exchanges is
that in a monetary economy exchanges are nonsynchronized—
the buying and the selling may occur at different times and in
different places.
3
Uncertainty
• If the value of money varies over time
(inflation), then this nonsynchronization of
exchanges amounts to risk.
• The need for money occurs because of time
and nonsychronization. Add uncertainty,
and you have potentially costly risk.
4
Equations of Exchange
I. Fisher Equation
M=money, T=real number of transactions,
VT =circular velocity of transactions
MVMT  PT T
II. Income-type Model/Commodities Approach
M=money, y=real income,
VY =circular velocity of income
MVMy  Py y
III. Cambridge Cash-Balances Equation
k = cash balances “constant”
M  kPy y
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Equations of Exchange (2)
IV. Disaggregation among components
D=demand deposits, Vdy=velocity of demand deposits
C=currency in hands of public, Vcy=velocity of currency
P=average
price of output
y
DVDy  CVCy  Py y
V. Cambridge Cash-Balances Equation
B = Monetary Base
k = cash balances “constant”
BVBy  Py y
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More on Quantity Theory
This really results from the system:
M s  M0
Ms Md
M d  kPY
Exogeneity of Money
Equilibrium Condition (ex post)
Money Demand Relation
Therefore, the crude quantity theory is
a theory of equilibrium absolute price levels.
Note: Not all quantity theorists assume exogeneity.
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Neoclassical Model
and the Quantity Theory
We begin with the “crude”, “old”, or “basic” quantity theory:
An exogenous change in the stock of money eventually
results in a proportionate change in the absolute price
level.
The Quantity Theory operates best in a Marshallian-type
neoclassical model.
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Marshallian Model
P
nominal
wages
w2
w1
w/P
LRAS
P2
AD2
P1
Y*
AD1
r
Y
S
r*
Ns
Nd
I
N
Y=F(N,K)
S*,I* S,I
Marshallian Model in Equations

s w
P

d w
P
d
(1) N  N ( )
s
(2) N d  N ( )
(3) N s ( wP )  N ( wP )  N *, ( wP ) *

(4) I  I (r )

(5) S  S (r )
(6) I (r )  S (r )  I *, S*, r *
(7) Y  F ( N*, K *)  Y *
(8) C  Y * S *  C  C (r*)  C *
(9) P  M 0
 P*
kY *
(10) ( wP ) *  P*  w *
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Fisher (1911)
• Fisher used the disaggregated model.
• Argued that the velocities are the “average rate of
turnover” and depends upon:
–
–
–
–
–
–
Individual agent habits
Population density (demographics)
Commercial customs
Rapidity of transport
Other technical conditions
But NOT on the quantity of money or the price level.
That is, velocity is EXOGENOUS.
• Fisher does not assume velocity is constant.
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Fisher (1911) -- II
• Fisher also argues that the real volume of trade or
transactions is independent of the quantity of money,
except during transition periods.
– This has been challenged by Keynesians. This is less likely to be
true if the economy is not continuously at equilibrium.
• Production is the result of capital, physical capabilities and
technique—none of which depend on the quantity of
money.
– This assumes that the labor market always clears and full
employment always ensues. It relies on the notion that full
employment is independent of money and prices.
• Therefore, if the quantity of money is expanded, prices will
rise. That is, prices will vary directly as M varies.
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Assumptions
(1) Money supply is exogenous.
(2) k and Y do not change substantially from one period to the
next. (Are they constant? Stable? Is the velocity function
stable?)
 Some argue that y is constant, based on the idea that the economy is
always at full employment.
 Some argue that y is constant because this is a long run theory and
Say’s Law does not allow for long-run deviations from full
employment.
 Some argue that k is relative constant because it is related to the
slowly evolving payments system.
 Some argue that k is simply exogenous—it is not related to any of the
other variables.
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Fisher’s Direct Transmission
Mechanism
• Fisher assumes that the individual’s money holdings are
doubled.
• “Prices being unchanged, he now has double the amount of
money and deposits which his convenience has now taught
him to keep on hand. He will then try to get rid of the
surplus money and deposits by buying goods. But, as
somebody else must be found to take the money off his
hands, its mere transfer will not diminish the amount in the
community. It will simply increase somebody else’s
surplus. Everybody will want to exchange this relatively
useless extra money for goods, and the desire to do so must
surely drive up the price of goods.”
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Indirect Transmission Mechanism
• Presented here only for contrast! This is NOT
Fisher’s view!
• According to the indirect mechanism, money
supply increases affect interest rates which then
induce changes in investment, which is a
component of aggregate demand. Aggregate
demand increases, driving the AD curve to the
right along an upward-sloping AS curve. Prices
rise.
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Cash Balances Approach
• This is a theory of money demand.
• Pigou argues that agents choose to allocate
resources to a portfolio of assets, based upon
convenience and security.
• The issue is the proportion allocated to money.
• k = k(r) – where r refers to the attractiveness of
“rival” uses of resources. As r increases, k falls.
• There is a discussion regarding the provision of
security against unexpected demands due to
sudden need or rise in prices.
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Knut Wicksell
• Defended the quantity theory as the
appropriate aggregate theory for the
determination of the price level.
– The alternative theory is called the “full cost
pricing theory” or the “mark-up price theory”.
Under this theory, the firms price according to
the cost of production plus a normal rate of
profit. In aggregate, this forms the price level.
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Knut Wicksell (2)
• Wicksell analyzed a “pure credit economy” which was short run with a
fixed capital stock.
– The public does not hold currency
– All transactions are paid for by checks drawn on demand accounts in
banks.
– Banks hold no reserves, so lend all deposits.
– Banks can lend without limit without risking insolvency.
– The market rate of interest is the rate charged by the banks.
– Banks are willing to lend any amount that firms want at the market rate of
interest.
– The normal rate of interest is the rate equates saving and investment.
– The natural rate of interest is the marginal productivity of investment in
firms, the internal rate of return on firms’ investment.
– He presented this in the context of a model of disaggregated output
(capital goods industries vs. consumer goods industries). In many ways he
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was a precursor of Keynes’ analysis.
Keynes
• Keynes identifies motives for holding
money:
–
–
–
–
Transactions demand
Precautionary demand
Speculative demand
Finance demand
• We will discuss Keynesian theory more
fully later in the course.
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Portfolio Approach
Agents allocate demand wealth across assets, of
which money is one:
M td  f (rtM , rtB , rt A ,..., wt )
This leads the money demand relations like:
Wt  M t  Bt  
20
Friedman’s Restatement of
the Quantity Theory
• Source: Studies in the Quantity Theory of Money, pp. 1-21.
• Quantity theory is a theory of money demand.
• Money is one of a variety of assets, a store of wealth or
value.
– Money is a factor in the production function; it is a capital good.
• The demand for money, like any other asset, depends upon:
–
–
–
–
Total wealth W
Price of and return on this and competing assets
Tastes and preferences
Intertemporal rates of substitution
21
More Elements
• Wealth relates to all sources of income or
consumable services:
–
Y = Wr
– So that
W = Y/r
– Where W = total wealth, Y = total income,
r = the rate of interest
• Agents allocate their wealth across assets so as to
maximize utility subject to costs and returns.
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More Elements
•
•
•
•
•
B = bonds
E = claims to stated pro-rata shares of firms
G = physical non-human goods
H = human capital
P = price level
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The Model
• Assume that the bonds are perpetuities, so that the
market price of the bond is:
1
PB 
rB
if the price is constant. If capital appreciation can
occur, the nominal return is:
 1 
d

rb (t ) 
rb (0) drb (t )

rb (0)  rb (0)
 rb (0)  2 
dt
rb (t ) dt
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The Model (2)
Which is approximated at t=0
1 drb
rb 
rb dt
• Rate of return on equities
1 dP 1 dre
re 

P dt re dt
• Rate of return on physical goods
1 dP
P dt
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The Model (3)
• Let w be the ratio of nonhuman to human
wealth.
• u is a portmonteau variable, which accounts
for all the other variables that might affect
tastes and preferences.
• Money demand is:

1 drb
1 dP 1 dre 1 dP Y 
M  f  P, rb 
, re 

,
; w, ; u 
rb dt
P dt re dt P dt
r 

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Model (4)
• Equivalently, we can write:

M  f P, RB , RE , RK , w, Y , u
r

• Arbitrage will lead RB= RE, or
1 drb
1 dP 1 dre
rb 
 re 

rb dt
P dt re dt
• Assuming the rates move together,
1 dP
rb  re 
P dt
(I = r +  )
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Model (5)
• Assume f() is homogeneous of degree one in P
and Y.
1 dP
f (P, rb , re ,
; w;Y ; u )
P dt
1 dP
 f ( P, rb , re ,
; w;Y ; u )
P dt
 f ( P, rb , re ,  ; w;Y ; u )
1
M
• Let   so that
 f (rb , re ,  , w, P , u )
Y
P
Y
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Model (6)
• This implies that:
Y
Y  v(rb , re ,  , w, , u )  M
P
• Note that this moves away from money as a
transactions medium, and toward money as
a portfolio asset.
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Conclusions
1. Money demand and velocity are highly stable. v
is not a constant, but rather a well-defined
function of a few specific variables.
2. Friedman regards money demand as playing the
key role in the determination of the whole
economy.
3. This amounts to a defense against the attacks of
Keynes that money demand and velocity are
unstable.
4. Money supply and demand are independent.
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Conclusions (2)
5. Implies there is not reason to assume that
money demand is infinitely elastic at some
small, positive, interest rate, and therefore
no support for a liquidity trap.
6. Argues that Y, as he has defined it, is
permanent income, and does not vary as
rapidly as measured income.
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Transmission Mechanisms
• Direct Transmission Channel
– Increases in the money supply causes undesired money balances
which are directly spent on commodities, increasing aggregate
expenditure and income.
• Indirect Transmission Channel (Keynes Effect)
– Increases in the money supply lowers the interest rate which
increases aggregate expenditure (think IS-LM) by increasing
investment and triggering the multiplier.
• The Lending Channel
– The availability of money causes banks to change their lending
practices, raising or lowering barriers to borrowing that may
involve more than interest rates.
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Walrasian-Type Model
There are n goods: x1, x2 ,..., xn
In a barter economy, there are n-1 relative prices
(exchange ratios) for each good:
p1 p1
p1
.
, ,...,
p2 p3
pn
We can consider money as xn 1 , so that the money
prices are:
pn
p1 p2
,
,...,
pn1 pn1
pn1
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Numeraire & Absolute Price Level
We define money as the numeraire good, and set pn1  1
so that money prices are:
p1, p2 ,...,. pn
The Absolute Price Level is a weighted average of the
money prices of the individual goods:
n
.
p   i pi
i 1
pn
p1 p2
, ,...,
We may define the relative prices as:
p p
p
which is essentially the prices in real terms.
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Neoclassical Model
and the Quantity Theory
The Quantity Theory operates best in a Marshallian-type
neoclassical model.
 Problem: Link between money and the goods market
 Problem: inconsistencies between the quantity theory and
Walrasian General Equilibrium Theory
• Highlighted by Patinkin (1965)
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Walrasian General Equilibrium
D
S
xiXD

x

x

i
i
Excess Demand
 = individual
xi = a good, the ith good
If there are  individuals, then in aggregate:


Or
 1
XD
xi


 1
D
xi


 1
S
xi
xiXD  xiD  xiS
is Aggregate Excess Demand.
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Walras’ Law
The sum of the excess demand and supplies over all markets
must identically equal zero. Equivalently,
n 1
XD
p
x
 i i  0.
i 1
Note: If there is an excess demand across the n goods markets,
then there must be an off-setting excess supply in the (n+1)th
market (for example in the money market).
XS
() pn1 xnXD

p
x
1
n 1 n .1
But if xn 1 is money, then pn1  1 .
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Walras’ Law (2)
Derivation:
Walras’ Law can be derived from the budget constraint. The budget constraint
essentially tells us that no individual can, through market trading, obtain a
greater value of goods and money (assets) than the initial endowment.
Homogeneity Postulate (typical assumption):
The demands and excess demands in the n goods markets will not change in
response to a change in the absolute price level.
Note: A homogeneous function x = f(y,z) is said to be homogeneous of degree 
with respect to y if and only if it has the property that:

 x  f (y, z ).
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Walras’ Law (3)
Note that homogeneity of degree one implies:
x  f (y, ,z )
which means that changes in y result in proportionate changes in
x. Homogeneity of degree zero implies that changes in y result in
no change in x.
Basic Elements of a Basic Walrasian GE Model
1. Walras’ Law
2. Excess demand equations
Excess demand equations are homogeneous of degree zero in
money prices and the absolute price level; i.e., the excess
demand equations obey the homogeneity postulate.
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Walrasian GE
and the Quantity Theory
Relative vs. Absolute Price levels
 The Quantity Theory determines the absolute price level, but not relative
prices.
 The Walrasian GE Model determines relative prices but not the absolute
price level.
QUESTION: Can we marry the two together?
This amounts to integrating microeconomic price theory with macroeconomic
monetary theory.
Can we add some form of the Equation of Exchange to the Walrasian
Model?
Answer: No. Patinkin demonstrates that such a model produces an invalid
dichotomy.
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WGE & Quantity Theory (2)
The model has n goods markets equilibrium equations, which we
assume are homogeneous of degree zero.
n
p
p
pi S  S
p

XD
i
n
1
xi  f i  ,..., ,..., ,  xi   xi  0.
p
p i 1 p 
p
It also has an equation to define the absolute price level:
n
pi
 i p  1
i 1
Add money demand:
MD = kpy
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WGE & Quantity Theory (3)
Subtract MS from both sides:
(1) M XD  kpy  M S  0
Link the M
XD
at equilibrium.
function with the real sector via Walras’ Law:
n
XD
XD
M

(

1
)
p
x
(2)
 i i because M is the n+1th good.
i 1
Unfortunately, this gives two excess demand functions for
money, and they are mutually inconsistent outside equilibrium:
(1) is nonhomogeneous to any degree.
(2) is homogeneous of degree one in prices.
42
Notes
Say’s Law
As a whole, S=D. Or equivalently,
n
XD
p
x
 i i  0.
i 1
• Walras’ Law includes the money market; Say’s Law is real
sector only.
• Walras’ Law: If there is a glut of goods, it is accompanied by
an excess demand for money.
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Patinkin’s Solution
Patinkin decides that only reasonable approach is to abandon
the homogeneity postulate (and Says’ Law).
Patinkin adds real balances throughout:
xiXD
 p1
pi
pn n pi S M S 
  xiS , i  1,..., n
 f i  ,..., ,..., ,  xi 
p
p i 1 p
p 
 p
thus demands and excess demands depend upon real
money balances!
44
Assume:
x XD
0
S
.


M


p


Unfortunately, this makes demands and excess demands a function
of the absolute price level. To maintain consistency throughout, we
write the money demand and money excess demand functions so as
to incorporate real balances:
S
 M 

M  pf n1  y,
p 

S


M
XD
  M S
M  pf n1  y,
p 

D
Money does prove neutral in this model.
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